REVIEW 1 cited by
Gauge transformation for the kinetic derivative nonlinear Schr\"odinger equation on the torus
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We consider the kinetic derivative nonlinear Schr\"odinger equation, which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. In our previous work, we proved small-data global well-posedness of the Cauchy problem on the torus in Sobolev space $H^s$ for $s>1/2$ by combining the Fourier restriction norm method with the parabolic smoothing effect, which is available in the periodic setting. In this article, we improve the regularity range to $s>1/4$ for the global well-posedness by constructing an effective gauge transformation. Moreover, we remove the smallness assumption by making use of the dissipative nature of the equation.
Forward citations
Cited by 1 Pith paper
-
Local well-posedness for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions
Derivative NLS around L∞ backgrounds, such as dark solitons, is unconditionally locally well-posed in H^s for s>3/4 under suitable background conditions.
Discussion (0). Continue with ORCID to comment.